Some global, analytical, and topological properties of regular black holes

Abstract

In this work, we study regular black holes from a global perspective, looking to evade some of the wellknown singularity theorems by using their "reverses." Then, model geometries for the slices of typical spherically symmetric, (locally) static four-dimensional regular black hole solutions are described from both an analytical and a topological point of view. While the finiteness of both the scalar and Kretchmann curvature of the slices around the regular center determines the geometry of the core, the positive answer to the Poincaré conjecture assures that, under two assumptions, its topology is that of a three-sphere. However, in general, the cores are shown to be S 3 , H 3 , R × S 1 , or S 1 × S 2 , depending on whether de Sitter, antide Sitter, Nariai, or Bertotti-Robinson geometries are employed to describe the slices at the regular center. Then, a description of the aforementioned slices in terms of Seifert fiber spaces is given in order to show that the Euler characteristic of the bundle can be used to track the transition between the core of the regular black hole and the rest of the slices in most of the cases considered in the literature. After Geroch and Tipler's theorems are employed to study the consequences of topology change on regular black hole spacetimes, we show that Borde and Vilenkin's singularity theorem is used to restrict their possible types. We end by noting that Nariai cores can be safely used to construct regular black holes without topology changes.

Singularity theorems for the Reissner-Nordström spacetime and topology change in regular black holes

“…This result reinforces some previous corollaries established in Ref. [7] to clarify whether topology change in regular black holes needs some asymptotically flat region in order to occur. This work is organized as follows.…”

“…Here we note that a plethora of regular black hole models showing the applicability of Theorem 1 have appeared in the literature [7,[18][19][20][21][22], most of them sharing an S 3 compact achronal slice as a common feature.…”

“…Let us recall that the previously mentioned results of Borde [2,3], which have had considerable impact with respect to the so-called regular black holes, i.e., geodesically complete spacetimes possessing trapped surfaces and inflationary cores, which essentially refers to black holes possessing a de Sitter-like structure substituting the singularity (see, for example, Refs. [7,17] and references therein), are based on the following "reversed" Penrose's theorem.…”

Ultracompact stars with polynomial complexity by gravitational decoupling

“…All of these solutions are known as BH mimickers and correspond to objects that, given their high compactness, the motion of test particles around them seems indistinguishable when compared with the physics around a BH (see [6], for a recent review). Some examples of BH mimickers found in literature encompasses regular BH [7][8][9], a e-mail: econtreras@usfq.edu.ec (corresponding author) traversable wormholes [10][11][12][13] and ultracompact stars [14], among others, and in this work we shall focus our attention in the latter.…”

Ultracompact stars with polynomial complexity by gravitational decoupling

“…All of these solutions are known as BH mimickers and correspond to objects that, given their high compactness, the motion of test particles around a e-mail: econtreras@usfq.edu.ec them seems indistinguishable when compared with the physics around a BH (see [6], for a recent review). Some examples of BH mimickers found in literature encompasses regular BH [7][8][9], traversable wormholes [10][11][12][13] and ultracompact stars [14], among others, and in this work we shall focus our attention in the latter.…”